Synchronization of a Novel Class of Fractional-Order Uncertain Chaotic Systems via Adaptive Sliding Mode Controller

Abstract

In this work an adaptive sliding mode controller in the presence of uncertainty, as well as the external disturbance is considered. A concise introduction and investigation of the dynamic behavior of a novel class of chaotic systems with fractional order derivatives for synchronization is presented. It is supposed that the high bounds of uncertainty and external disturbance are unknown. The proposed controller is designed based on error dynamics and acceptable adaptive laws. The sliding mode dynamic stability and the condition to start sliding are proved by Lyapunov stability theory. With this new proposed approach, Chen and Lorenz system with fractional order derivatives are synchronized. Finally, simulation results with MATLAB software showed that the designed comparative sliding mode controller was able to synchronize chaotic systems with fractional order derivatives in the presence of the mentioned adverse factors. The main characteristic of the proposed method compared to other methods is providing acceptable adaptive laws for satisfactory functioning against uncertainty and external disturbance and eliminate the chattering phenomenon for synchronization of non-identical chaotic systems with fractional order derivatives.

Sliding mode disturbance observer control based on adaptive synchronization in a class of fractional‐order chaotic systems

“…For the nameless disturbances, it can be approximated by choosing the appropriate control gain parameter well. An ASMC is presented in the work of Riahi et al 27 for synchronization of chaotic systems with fractional-order derivatives in the presence of uncertainty and external disturbance. A summary introduction and examination of the dynamic behavior of a new class of chaotic systems with fractional-order derivatives for synchronization is presented.…”

“…Theorem 1. Presume that the sliding surface is defined as (27) and the disturbance-observer is designed as (13). Then, the synchronization errors (25) are bounded and stable under ASMC schemes as (29) and (31).…”

Adaptive H∞ Observer‐Based Sliding Mode Control for Uncertain Fractional‐Order Nonlinear Systems

“…A dynamic SMC was proposed for the single input nonlinear fractional order system with system model uncertainties [14]. An active SMC was designed to synchronize fractional order chaotic systems with unknown parameters, non-linear input and external disturbance [15,16]. An adaptive backstepping SMC scheme on finite-time scheme was proposed for uncertain fractional-order nonlinear systems [17].…”

Adaptive synchronization of fractional-order quadratic chaotic flows with nonhyperbolic equilibrium

“…Hence, synchronization of the fractional-order chaotic systems with uncertainties is a vital research subject. The fractional-order chaotic systems, as a generalization of integer-order chaotic systems, are considered as alternatives for which significant attentions have been encouraged on increasing techniques for modeling, control, or synchronization of this class of generalized dynamic systems (Yin et al., 2012a; Riahi et al., 2016; Wang and Qi, 2016).…”

“…(2016), a fractional-order disturbance observer based on ASMC synchronization is recommended for fractional-order chaotic systems with unknown bounded disturbances. An ASMC is presented in Riahi et al. (2016) for synchronization of chaotic systems with fractional-order derivatives in the sense of uncertainty and external disturbance.…”